Gauge Fixing and the Gibbs Phenomenon

Details Gauge Fixing and the Gibbs Phenomenon Gauge Fixing and the Gibbs Phenomenon

1998-10-19

arxiv.org/abs/hep-lat/9810038v1

Nucl.Phys.Proc.Suppl. 73 (1999) 883-885

Physics

High Energy Physics

High Energy Physics - Lattice

3 Pages; Talk at Lattice '98; Postscript version only - not available in tex

Scientific paper

10.1016/S0920-5632(99)85233-5

We address the question of why global gauge fixing, specifically to the lattice Landau gauge, becomes an extremely lengthy process for large lattices. We construct an artificial "gauge-fixing" problem which has the essential features encountered in actuality. In the limit in which the size of the system to be gauge fixed becomes infinite, the problem becomes equivalent to finding a series expansion in functions which are related to the Jacobi polynomials. The series converges slowly, as expected. It also converges non-uniformly, which is an observed characteristic of gauge fixing. In the limiting example, the non-uniformity arises through the Gibbs phenomenon.

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